Problem: The sum of two numbers is $30$, and their difference is $6$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 30}$ ${x-y = 6}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 36 $ $ x = \dfrac{36}{2} $ ${x = 18}$ Now that you know ${x = 18}$ , plug it back into $ {x+y = 30}$ to find $y$ ${(18)}{ + y = 30}$ ${y = 12}$ You can also plug ${x = 18}$ into $ {x-y = 6}$ and get the same answer for $y$ ${(18)}{ - y = 6}$ ${y = 12}$ Therefore, the larger number is $18$, and the smaller number is $12$.